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Finding the Third Proportional to 284 and 409.75

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Solution

The third proportional to 284 and 409.75 is: 591.18

Step by Step Solution

  1. Step 1: Write the proportion equation
    284 : 409.75 = 409.75 : x
  2. Step 2: Convert to fraction form
    284/409.75 = 409.75/x
  3. Step 3: Cross multiply
    284x = 409.75 × 409.75
  4. Step 4: Simplify right side
    284x = 167,895.06
  5. Step 5: Solve for x
    x = 167,895.06/284
  6. Step 6: Final answer
    x = 591.18

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Why These Related Problems?

These problems maintain the same ratio (1.44) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.